Effects of Linear Transformations
- Define a linear transformation
- Compute the mean of a transformed variable
- Compute the variance of a transformed variable
This section covers the effects of linear transformations
on measures of central tendency and variability.
If a variable X has a mean of μ, a standard
deviation of σ, and a variance of σ2,
then a new variable Y created using the linear transformation
Y = bX + A
will have a mean of bμ+A,
a standard deviation of bσ, and a
variance of b2σ2.